GEXAMPLE $4$

A $45$ strain rosette is fitted to the exterior skin of the fuselage of a pressurized aircraft. The fuselage material is AL$7074$Tb$,$ with $E=10,000$ksi,$v=0\mathrm{.}3,$ and $y=64$ksi. At a $3$ psi pressure differential, the readings of the strain gages are $a=1262i\frac{n}{i}n,b=822i\frac{n}{i}n,$ and $c=758i\frac{n}{i}n.$

According to the Tresca yield criterion, does the Aluminum yield at the $3$ psi pressure differential? If not, what pressure could cause it to yield? Repeat these questions for the von Mises yield criterion.